1. What is Chi-square P-value?

The Chi-square p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. It's used in Chi-square tests to determine statistical significance.

2. How Does the Calculator Work?

The calculator uses the Chi-square distribution formula:

Where:

• \( \chi^2 \) — Chi-square test statistic
• \( df \) — Degrees of freedom
• \( \chi^2_{cdf} \) — Chi-square cumulative distribution function

Explanation: The p-value is calculated as the complement of the cumulative distribution function for the given Chi-square value and degrees of freedom.

3. Interpretation of P-value

Details: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, while a large p-value suggests weak evidence against the null hypothesis.

4. Using the Calculator

Tips: Enter the Chi-square test statistic and degrees of freedom. Both values must be positive numbers (degrees of freedom must be ≥1).

5. Frequently Asked Questions (FAQ)

Q1: What is a Chi-square test used for?
A: Chi-square tests are used to examine relationships between categorical variables or to test goodness-of-fit.

Q2: What does degrees of freedom mean?
A: Degrees of freedom depend on the number of categories in your data. For a contingency table, df = (rows-1)*(columns-1).

Q3: What's considered a statistically significant p-value?
A: Typically p ≤ 0.05 is considered statistically significant, but this threshold depends on your field of study and specific requirements.

Q4: Can I use this for very large Chi-square values?
A: The calculator should work for most practical values, but extremely large values might lead to precision limitations.

Q5: How accurate is this calculator?
A: The calculator provides a good approximation, but for critical applications, consider using specialized statistical software.